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  Lesson Plans
Picking Pythagoras

Alexander Sabatino, Jr.
OverviewProcedure for teachersStudent Resources and Materials
Grade Level
 6-9
Time Alloment
 Five 45-minute classes

Overview

This is an interactive media-rich lesson in which students examine the Pythagorean Theorem. By experiment, students will discover that side measurement is important in determining the angle classification of a triangle. By squaring sides, they will predict whether triangles will be right, obtuse, or acute. Using the Internet, students will prove the Pythagorean Theorem and use it to solve problems. Finally, students will demonstrate their knowledge of the Pythagorean Theorem by finding the perimeter of polygons on the coordinate plane by triangulation. This lesson utilizes reading, writing, and mathematical skills in an interdisciplinary format.


Learning Activities

Students will be able to:
  • Prove that the sum of two sides of a triangle must be greater than the third
  • Use the Pythagorean Theorem to predict triangle classification by angle
  • Use a calculator to find a square root to the nearest tenth
  • Find the missing side of a right triangle
  • Apply the Pythagorean Theorem in problem solving
  • Use triangulation to find the perimeter of a polygon on the coordinate plane

Standards

National Council of Teachers of Mathematics grades K-12
http://www.nctm.org/standards/standards.htm

Number and Operations
  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

  • Compute fluently and make reasonable estimates.
Algebra
  • Represent and analyze mathematical situations and structures using algebraic symbols.

  • Use mathematical models to represent and understand quantitative relationships.
Geometry
  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

  • Apply transformations and use symmetry to analyze mathematical situations.

  • Use visualization, spatial reasoning, and geometric modeling to solve problems.
Measurement
  • Apply appropriate techniques, tools, and formulas to determine measurements.
Data Analysis and Probability
  • Develop and evaluate inferences and predictions that are based on data.
Problem Solving
  • Solve problems that arise in mathematics and in other contexts.

  • Apply and adapt a variety of appropriate strategies to solve problems.
Reasoning and Proof
  • Make and investigate mathematical conjectures.
Communication
  • Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Connections
  • Recognize and apply mathematics in contexts outside of mathematics.

Media Components

Web sites:

Nova: The Proof, The Pythagorean Puzzle, Demonstrate the Pythagorean Theorem

http://www.pbs.org/wgbh/nova/proof/puzzle/papertriangle.html
This site has a printable right triangle on a grid.

Nova: The Proof, The Pythagorean Puzzle, Demonstrate the Pythagorean Theorem
http://www.pbs.org/wgbh/nova/proof/puzzle/theoremsans.html
Students can prove the Pythagorean Theorem by drawing and cutting squares on the sides of a right triangle and showing that the smaller squares together equal the larger square.

International Education Software, Pythagorean Theorem #1
http://www.ies.co.jp/math/Java/geo/pythasvn/pythasvn.html
A Japanese educational group maintains this site. They offer Java applets demonstrating various mathematical topics. In Pythagorean Theorem #1, students create a right triangle by moving a red dot. Squares are drawn on all three sides. The two smaller squares are cut into polygons that change shape as the triangle changes. Students move the polygons inside the two smaller squares into the largest square proving the Pythagorean Theorem. To run the demonstrations, you must have Java enabled on your computer.

University of Minnesota Geometry Center, Pythagorean Applications, Baseball Problem
http://www.geom.umn.edu/~demo5337/Group3/bball.html
This is a good site to get applications of math topics. The center presents students a problem in baseball where they have to apply the Pythagorean Theorem.

International Education Software, Pythagoras Tree
http://www.ies.co.jp/math/Java/geo/pytree/pytree.html
Students create a right triangle by moving a red dot. Squares are drawn on the triangle and each subsequent click on the button creates right triangles and squares on the previous squares. In order to work, your computer must be Java-enabled.

Nova Online Adventure Web Site
http://www.pbs.org/wgbh/nova/pyramid/geometry/model.html
On this site, students assemble a scale paper model of the great pyramid using a printable copy of a diagram. The measurements of two more Egyptian pyramids are given for the class to scale down and assemble from scratch. Students use the Pythagorean Theorem to obtain scale measures of the pyramid's sides.


Materials

Per Class:
  • Set of calculators
  • Set of rulers
  • Set of scissors
  • 12 to 15 Triangle Activity Packets
  • 12 to 15 paper clips
Per student:
  • 1-2 sheets of quarter-inch graph paper
  • Right triangle on grid paper
  • Exploring Angles Activity
  • Triangle Classification Organizer
  • Triangulation Sampler Organizer